No. Stuff like UK rail privatization or US electricity deregulation happened.
It's just that today, even in die-hard free market countries, people have come to realize that infrastructure and private/for-profit don't mix well most of the time.
A necessary part of a free market is that consumers have choice. In the franchised UK rail system, there are very few routes on which one can choose between different suppliers. The franchise system also imposes huge barriers to new entrants to the market. Therefore, there is little incentive for companies, having won the franchise, to improve the service more than the minimum necessary.
The core infrastructure of the UK rail network is still owned and run by Network Rail, which is publicly owned, so the core inefficiencies remain.
The private operators compete for the contract to run a franchise for a couple of years. The "choice" is not for the passenger, the choice is for the government to decide which private company to give the franchise, to give access to the infrastructure, and to provide subsidies. The competition basically happens at the bidding level.
NYC is a great example. In exchange for access, two companies signed contracts with the city that limited prices to $0.05. They built a large portion of the existing lines and made a good chunk of change.
But the City wanted to own them, and inflation stepped into the picture decades later. Turns out, a nickel wasn't worth the same anymore and couldn't cover costs. Rather than allow prices to rise, the City bought up the two companies while building a third system (the IND). It also doubled fares after unifying. Hmm....
Then it put out an elected board to vote on fare increases. Guess what the winning stance was? No increase. Eventually the system decayed as the subsidies didn't cover maintenance and deferred maintenance eventually became a major issue. The system today still has 1930s and 50s technology.
If anything, the US public transit systems (which had similar stories in other cities) are evidence against American governments running infrastructure.
We are underfunding other important pieces of infrastructure from roads to bridges to sewers, so the next few decades should be fun as cheaply built suburbs deal with infrastructure costs rising.
Oh, and fares have increased many many times. Many people always complain when it does.
And NYC is still building new subway lines. Construction is underway right now on a new east side line.
In any case, the two private systems are badly designed relative to one another: bad transfers, redundancies. The IND built by the public is overall much better designed.
The fact that both the private and public where able to build giant subway systems in the 10s-40s but it all fell apart after, should give some idea that it wasn't anything inherent to being public or private that allowed building it and made it difficult later, but other factors.
It's too bad. Because singapore, which arguably has the world's best (or maybe second best, after Seoul) public transit system, is basically an entirely privatized system.
The public Land Transport Authority built and still owns most of the assets, and enacts strong regulation for the duopoly of service providers (SBS and SMRT) - not only on service levels, but also on operational processes. Even so, there's awkward UX quirks on the boundaries between lines run by the different companies.
If anything, the Singapore MRT runs closer in spirit to a US taxicab system - that is, surprisingly regulated on a global scale.
Comfortdelgro is certainly widely owned - but they're into busses and taxi mainly, not infra heavy stuff like subways.
For various reasons, Governments will make state owned companies publically traded. That doesn't mean they're not going to toe the government line in decisions if it has majority stake.
I wasn't aware that SMRT was bought out by the government recently (the last time I rode the MRT, last year, it was still private). It doesn't seem that the buyout was orchestrated as some sort of bailout, especially given that the systems seem to be solvent enough to support at least one for-profit. It, then, remains to be seen if refolding SMRT will result in a net degradation or net improvement in services... This will be an interesting 'control' experiment.
The UK STILL has not solved its problem of wrong tracks and seemingly never will, trains are still absurdly expensive compared to cars and the government still ploughs billions of pounds into what is supposed to be a "privatised" system. Its fucked.
Our only future transport hope in this country is automated cars.